Zhen Lei
Abstract
We characterize strongly regular rings via generalized weakly ideals.The following conditions are shown to be equivalent: ① R is a strongly regular ring;② R is a semi-prime left GP-V′-ring whose every maximal left ideal is generalized weakly ideal of R;③ R is a semi-prime left GP-V′-ring whose every maximal right ideal is generalized weakly ideal of R.
A significance statement is not available in the OpenAlex record.
A contribution statement is not available in the OpenAlex record.
Method details are not available in the OpenAlex metadata.
Findings are not separately available in the OpenAlex metadata.
Limitations are not available in the OpenAlex metadata.
Application details are not available in the OpenAlex metadata.
We characterize strongly regular rings via generalized weakly ideals.The following conditions are shown to be equivalent: ① R is a strongly regular ring;② R is a semi-prime left GP-V′-ring whose every maximal left ideal is generalized weakly ideal of R;③ R is a semi-prime left GP-V′-ring whose every maximal right ideal is generalized weakly ideal of R.
Key concepts: Mathematics, Ideal (ethics), Maximal ideal, Prime (order theory), Ring (chemistry), Minimal ideal, Prime ideal, Reduced ring